BOD (Biochemical Oxygen Demand) Calculator
Compute BOD₅ from dilution test data, estimate ultimate BOD (BODu), and determine the deoxygenation rate constant k using standard first‑order BOD kinetics.
BOD₅ from Dilution Test
Use this mode when you have dissolved oxygen (DO) readings from a standard 5‑day BOD test with dilution water and a blank.
If left blank, seed correction is ignored.
What is biochemical oxygen demand (BOD)?
Biochemical oxygen demand (BOD) is the amount of dissolved oxygen (DO) that microorganisms consume while decomposing biodegradable organic matter in water under specified conditions. It is a key indicator of organic pollution and wastewater strength.
The most common test is the 5‑day BOD at 20 °C, denoted BOD₅. For design and modeling, the ultimate BOD (BODu) and the deoxygenation rate constant k are often used.
1. BOD₅ from dilution test – formula
In a standard dilution BOD test, a known volume of sample is diluted with oxygen‑saturated dilution water, seeded if necessary, and incubated for 5 days at 20 °C. BOD₅ is calculated from the DO depletion.
General formula (with blank and seed correction):
\[ \text{BOD}_5 = \bigl(D_1 - D_2 - B \times f\bigr) \times \frac{V_\text{bottle}}{V_\text{sample}} \]
- \(D_1\) = initial DO of diluted sample (mg/L)
- \(D_2\) = DO after 5 days (mg/L)
- \(B\) = DO depletion in the blank = \(D_{1,\text{blank}} - D_{2,\text{blank}}\) (mg/L)
- \(f\) = seed correction factor = (seed in sample) / (seed in blank)
- \(V_\text{bottle}\) = volume of BOD bottle (mL or L)
- \(V_\text{sample}\) = volume of sample in bottle (mL or L)
If no seed correction is needed (e.g., seeded dilution water is not used or its effect is negligible), the formula simplifies to:
\[ \text{BOD}_5 = \bigl(D_1 - D_2\bigr) \times \frac{V_\text{bottle}}{V_\text{sample}} \]
Worked example
Suppose:
- Bottle volume = 300 mL
- Sample volume = 15 mL
- Sample DO: D₁ = 8.5 mg/L, D₂ = 2.1 mg/L
- Blank DO: D₁,blank = 8.7 mg/L, D₂,blank = 8.4 mg/L → B = 0.3 mg/L
- Seed factor f = 1.0
Then:
\[ \text{BOD}_5 = \bigl(8.5 - 2.1 - 0.3 \times 1.0\bigr) \times \frac{300}{15} = (6.1)\times 20 = 122\ \text{mg/L} \]
2. Ultimate BOD (BODu) and first‑order kinetics
The biochemical oxidation of organic matter is often modeled as a first‑order reaction:
\[ \text{BOD}_t = L_0 \bigl(1 - e^{-k t}\bigr) \]
- \(\text{BOD}_t\) = BOD exerted at time \(t\) (mg/L)
- \(L_0\) = ultimate BOD (BODu) (mg/L)
- \(k\) = deoxygenation rate constant (day⁻¹)
- \(t\) = time (days)
Solving for BODu from BOD₅ and k
Rearranging the first‑order equation:
\[ L_0 = \frac{\text{BOD}_t}{1 - e^{-k t}} \]
For example, if BOD₅ = 200 mg/L and k = 0.23 day⁻¹:
\[ L_0 = \frac{200}{1 - e^{-0.23 \times 5}} \approx \frac{200}{1 - e^{-1.15}} \approx \frac{200}{1 - 0.316} \approx \frac{200}{0.684} \approx 292\ \text{mg/L} \]
Solving for k from BOD₅ and BODu
If BODu is known (e.g., from long‑term tests), k can be estimated as:
\[ k = -\frac{1}{t}\,\ln\!\left(1 - \frac{\text{BOD}_t}{L_0}\right) \]
3. Interpreting BOD values
Typical BOD₅ ranges (approximate):
- Pristine surface water: < 2 mg/L
- Good quality river: 2–3 mg/L
- Moderately polluted river: 3–5 mg/L
- Heavily polluted river: > 8 mg/L
- Treated municipal effluent: 10–30 mg/L
- Raw municipal sewage: 150–300+ mg/L
High BOD indicates a high concentration of biodegradable organic matter. If BOD is too high, dissolved oxygen in receiving waters can be depleted, stressing or killing aquatic life.
4. Practical notes and limitations
- BOD tests are sensitive to temperature, incubation time, and microbial activity.
- Nitrification can contribute to oxygen demand; nitrification inhibitors are often used for CBOD tests.
- Highly toxic or very strong industrial wastes may require special dilution and seeding procedures.
- The first‑order model is an approximation but is widely used for design and river DO sag analysis.
This calculator is for educational and preliminary design use only. For regulatory compliance, always follow the relevant standard methods (e.g., APHA Standard Methods, national regulations) and your laboratory’s QA/QC procedures.